For a reduced knot diagram with two adjacent starred regions, a Kauffman state chooses one corner at every crossing so that every unstarred region contains exactly one chosen corner. Terms in a determinant expansion of a Dehn-presentation Alexander matrix correspond bijectively to these states.

Ancestors (11)

  1. Alexander matrix
  2. Alexander polynomial of a knot
  3. Seifert matrix
  4. Seifert form
  5. Seifert surface
  6. Knot
  7. Knot theory
  8. Geometry and topology
  9. Area of mathematics
  10. Mathematics
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